• ON THE ADDITIVE AND MULITIPLICATIVE STRUCTURE OF SEMIRINGS

Abstract

Addittive and multiplicative structures play an important role in determining the sturcutre. A semiring is said to be a  Positive Rational Domain (PRD) if(S,×)  is a commutative group. If S is a PRD and x Ï x + S and  x Ï S + x, then  (S,+)  is positively ordered in strict sense or negatively ordered in strict sense or negatively ordered in strict sense . Also it is proved that in a PRD, (S,+) is positively ordered in strict sense or negatively ordered in strict sense if (S,+)   is cancellative. In a PRD if E[+] is nonempty then E[+] is a completely prime multilplicative ideal. Also we study the properties of semirings.